System for controlling synchronous motor

ABSTRACT

A control apparatus includes a current detector which detects a current of a synchronous motor, a coordinate converter which coordinate-converts the current obtained from the current detector into a current on rotational biaxial coordinates (d-q axis) rotated at an angular frequency w, a current controller which outputs a voltage command on the rotational biaxial coordinates (d-q axis) such that a current on the rotational biaxial coordinates (d-q axis) follows a current command on the rotational biaxial coordinates (d-q axis), a coordinate converter which coordinate-converts the voltage command on the rotational biaxial coordinates (d-q axis) obtained from the current controller into three-phase voltage commands, an adaptive observer which calculates the angular frequency w, an estimated current of the synchronous motor, an estimated rotor magnetic flux, and an estimated rotational speed based on the current on the rotational biaxial coordinates (d-q axis) and the voltage command on the rotational biaxial coordinates (d-q axis), and an inverter which applies a voltage to the synchronous motor based on the voltage command. The adaptive observer calculates the angular frequency w such that a q-axis component of the estimated rotor magnetic flux is zero.

TECHNICAL FIELD

[0001] The present invention relates to a control apparatus whichcontrols a synchronous motor without using a position sensor.

BACKGROUND ART

[0002] In general, a position sensor such as an encoder, a resolver, ora hall element is required to control a synchronous motor. However, theposition sensor is disadvantageously used in a control apparatus for asynchronous motor with respect to prices, the reliability of the sensor,cumbersome wiring, and the like. From this viewpoint, a method ofcontrolling a synchronous motor without using a position sensor has beenproposed.

[0003] For example, as a method of calculating a rotational position anda rotational speed of a synchronous motor based on a mechanical constantsuch as an inertia, an induced voltage coefficient determined by amagnet magnetic flux or the like, and electric constants such as aninductance and a resistance of the synchronous motor, inventionsdisclosed in U.S. Pat. No. 5,296,793, U.S. Pat. No. 5,296,794, JapanesePatent Application Laid-Open No. 03-049589, Japanese Patent ApplicationLaid-Open No. 03-049588, and the like are known.

[0004] As a method of calculating a rotational position and a rotationalspeed of a synchronous motor based on an induced voltage coefficientwhich is a function of a rotor magnetic flux such as a magnet magneticflux and an electric constant such as an inductance and a resistance ofthe synchronous motor, inventions disclosed in Japanese PatentApplication Laid-Open No. 08-308286, Japanese Patent ApplicationLaid-Open No. 09-191698, and the like are known.

[0005] However, even though these methods are used, a mechanicalconstant such as an inertia is unknown, or controllability isdeteriorated when degauss of a magnet magnetic flux is caused by heatgeneration from an electric motor.

[0006] On the other hand, the control method which can solve the aboveproblems without requiring an induced voltage coefficient which is afunction of a mechanical constant such as an inertia or a rotor magneticflux such as a magnet magnetic flux is proposed in, e.g., “Position andSpeed Sensorless Control of Brush-Less DC Motor Based on an AdaptiveObserver” The Journal of The Institute of Electrical Engineers of JapanVol. D113, No. 5 (1993).

[0007]FIG. 15 shows a conventional control apparatus for a synchronousmotor described in The Journal of The Institute of Electrical Engineersof Japan Vol. D113, No. 5. In this figure, reference numeral 1 denotes asynchronous motor, 2 denotes a current detector, 3 denotes an inverter,4 denotes a current controller, 5 to 8 denote coordinate converters, 9denotes an adaptive observer, and 10 denotes a rotational positioncomputing unit.

[0008] The synchronous motor 1 has a permanent magnet as a rotor whichhas a rotor magnetic flux of pdr. An inductance Ld in the direction ofthe rotor magnetic flux (d-axis direction) is equal to an inductance Lqin a direction (q-axis direction) perpendicular to the direction of therotor magnetic flux. These inductances are L each. A wire woundresistance of the synchronous motor 1 is R.

[0009] As is well known, when a synchronous motor is vector-controlled,an arbitrary value has been given as a d-axis current command id* on arotational biaxial coordinate axis (d-q axis) in advance. As a q-axiscurrent command iq* on the rotational biaxial coordinate axis (d-qaxis), a value which is in proportional to a desired torque of thesynchronous motor 1 has been given in advance.

[0010] The current controller 4 outputs a d-axis voltage command vd* anda q-axis voltage command vq* on the rotational biaxial coordinate axis(d-q axis) such that detection currents id and iq on the rotationalbiaxial coordinate axis (d-q axis) rotated in synchronism with arotational position output from the rotational position computing unit10 follow the d-axis current command id* and the q-axis current commandiq*, respectively.

[0011] The coordinate converter 5 coordinate-converts the d-axis voltagecommand vd* and the q-axis voltage command vq* on the rotational biaxialcoordinate axis (d-q axis) into an a-axis voltage command va* and ab-axis voltage command vb* on static biaxial coordinates (a-b axis)based on a cosine cos(th0) and a sine sin(th0) obtained from therotational position computing unit 10.

[0012] The coordinate converter 6 coordinate-converts the a-axis voltagecommand va* and the b-axis voltage command vb* on the static biaxialcoordinates (a-b axis) into three-phase voltage commands vu*, vv* andvw*. The inverter 3 applies three-phase voltages to the synchronousmotor 1 in accordance with the three-phase voltage commands vu*, vv* andvw* obtained from the coordinate converter 8.

[0013] The current detectors 2 detect a U-phase current iu and a V-phasecurrent iv of the synchronous motor 1. The coordinate converter 7coordinate-converts the U-phase current iu and the V-phase current ivobtained from the current detectors 2 into an a-axis current ia and ab-axis current ib on the static biaxial coordinates (a-b axis).

[0014] The coordinate converter 8 outputs the a-axis current ia and theb-axis current ib on the static biaxial coordinates (a-b axis) and ad-axis current command id and a q-axis current command iq on therotational biaxial coordinate axis (d-q axis) based on a cosine cos(th0)and a sine sin(th0) obtained from the rotational position computing unit10.

[0015] The adaptive observer 9 outputs an a-axis estimated rotormagnetic flux par0 and a b-axis estimated rotor magnetic flux pbr0 onthe static biaxial coordinates (a-b axis) and an estimated rotationalspeed wr0 based on the a-axis voltage command va* and the b-axis voltagecommand vb* on the static biaxial coordinates (a-b axis) and the a-axiscurrent ia and the b-axis current ib on the static biaxial coordinates(a-b axis).

[0016] The rotational position computing unit 10 calculates the cosinecos(th0) and the sine sin(th0) of a rotational position th0 of anestimated magnetic flux vector from the a-axis estimated rotor magneticflux par0 and the b-axis estimated rotor magnetic flux pbr0 on thestatic biaxial coordinates (a-b axis) according to the followingequations (1) to (3), $\begin{matrix}{{\cos ({th0})} = \frac{par0}{pr0}} & (1) \\{{\sin ({th0})} = \frac{pbr0}{pr0}} & (2)\end{matrix}$

pr0={square root}{square root over (par ² +pbr0²)}  (3)

[0017]FIG. 16 is a diagram which shows the internal configuration of theadaptive observer 9 shown in FIG. 15. In this figure, reference numeral11 denotes an electric motor model, 12 and 13 denotes subtractors, 14denotes a speed identifier, 15 denotes a gain computing unit, and 16denotes a deviation amplifier.

[0018] The electric motor model 11 calculates an a-axis estimatedcurrent ia0 and a b-axis estimated current ib0 on the static biaxialcoordinates (a-b axis) and the a-axis estimated rotor magnetic flux par0and the b-axis estimated rotor magnetic flux pbr0 based on the a-axisvoltage command va* and the b-axis voltage command vb* on the staticbiaxial coordinates (a-b axis), the estimated rotational speed wr0, anddeviations e1, e2, e3, and e4 (to be described later) according to thefollowing equation (4), $\begin{matrix}{{\frac{}{t}\begin{pmatrix}\begin{matrix}\begin{matrix}{ia0} \\{ib0}\end{matrix} \\{par0}\end{matrix} \\{pbr0}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{L}} & 0 & 0 & \frac{wr0}{L} \\0 & {- \frac{R}{L}} & {- \frac{wr0}{L}} & 0 \\0 & 0 & 0 & {- {wr0}} \\0 & 0 & {wr0} & 0\end{pmatrix}\begin{pmatrix}\begin{matrix}\begin{matrix}{ia0} \\{ib0}\end{matrix} \\{par0}\end{matrix} \\{pbr0}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{L} & 0 \\0 & \frac{1}{L} \\0 & 0 \\0 & 0\end{pmatrix}\left( \begin{matrix}{va}^{*} & \quad \\v^{*} & \quad\end{matrix}\quad \right)} - \begin{pmatrix}{e1} \\{e2} \\{e3} \\{e4}\end{pmatrix}}} & (4)\end{matrix}$

[0019] The subtractor 12 outputs a result obtained by subtracting thea-axis current ia from the a-axis estimated current ia0 as an a-axiscurrent deviation ea. The subtractor 13 outputs a result obtained bysubtracting the b-axis current ib from the b-axis estimated current ib0as a b-axis current deviation eb.

[0020] The speed identifier 14 outputs the estimated rotational speedwr0 based on the Par0, pbr0, ea, and eb according to the followingequation (5), $\begin{matrix}{{wr0} = {\left( {{kp} + \frac{ki}{s}} \right)\left( {{{ea} \cdot {pbr0}} - {{eb} \cdot {par0}}} \right)}} & (5)\end{matrix}$

[0021] The gain computing unit 15 outputs gains g1, g2, g3, and g4 basedon the estimated rotational speed wr0 according to the followingequations (6) to (9), $\begin{matrix}{{g1} = {{- \left( {k - 1} \right)}\frac{R}{L}}} & (6)\end{matrix}$

 g2=(k−1)wr0  (7)

g3=k R  (8)

g4=−k L wr0  (9)

[0022] where k is an arbitrary real number larger than 1.

[0023] The deviation amplifier 16 amplifies the current deviations eaand eb by the gains g1, g2, g3, and g4 to output the deviations e1, e2,e3, and e4. More specifically, the deviation amplifier 16 outputs thedeviations e1, e2, e3, and e4 to the electric motor model 11 accordingto the following equation (10), 1, an inductance on static biaxialcoordinates changes depending on the position of a rotor.

[0024] The conventional control apparatus for a synchronous motorconstitutes an adaptive observer on static biaxial coordinates andcannot handle an inductance as a constant value. For this reason, thecontrol apparatus cannot be easily applied to the synchronous motor.

[0025] In the conventional control apparatus for a synchronous motor,gains g1, g2, g3, and g4 are determined such that the pole of theadaptive observer is in proportion to the pole of the synchronous motor.However, when the synchronous motor is driven at a low rotational speed,the pole of the adaptive observer decreases because the pole of thesynchronous motor is small. Therefore, the response of an estimatedmagnetic flux is deteriorated, the characteristics of the control systemitself is also deteriorated.

[0026] The feedback gains g1, g2, g3, and g4 are set such that the poleof the adaptive observer 9 is in proportion to the unique pole of thesynchronous motor 1. However, when an estimated rotational speeddeviates from an actual rotational speed, these gains are notappropriate to perform state estimation. For this reason, the actualrotational speed wr deviates from the estimated rotational speed wr0,and thereby the accuracy of magnetic flux estimation is deteriorated.

[0027] Therefore, it is an object of the present invention to provide acontrol apparatus for a synchronous motor which can constitute anadaptive observer on rotational two axes and can control the synchronousmotor at a high rotational speed.

DISCLOSURE OF THE INVENTION

[0028] The control apparatus for a synchronous motor according to thepresent invention comprises a current detector which detects a currentof a synchronous motor, a coordinate converter which coordinate-convertsthe current obtained from the current detector into a current onrotational biaxial coordinates (d-q axis) rotated at an angularfrequency, a current controller which outputs a voltage command on therotational biaxial coordinates (d-q axis) such that a current on therotational biaxial coordinates (d-q axis) follows a current command onthe rotational biaxial coordinates (d-q axis), a coordinate converterwhich coordinate-converts the voltage command on the rotational biaxialcoordinates (d-q axis) obtained from the current controller intothree-phase voltage commands, an adaptive observer which calculates theangular frequency, an estimated current of the synchronous motor, anestimated rotor magnetic flux, and an estimated rotational speed basedon the current on the rotational biaxial coordinates (d-q axis) and thevoltage command on the rotational biaxial coordinates (d-q axis), and aninverter which applies a voltage to the synchronous motor based on thevoltage command. The adaptive observer calculates the angular frequencysuch that a q-axis component of the estimated rotor magnetic flux iszero.

[0029] According to this invention, since the adaptive observercalculates the angular frequency such that the q-axis component of theestimated rotor magnetic flux is zero, the adaptive observer can beconstituted on the rotational two axes.

[0030] In the control apparatus for a synchronous motor according to thenext invention based on the above invention, the adaptive observer hasan electric motor model in which a salient-pole ratio is not 1.

[0031] According to this invention, since the adaptive observer has theelectric motor model in which the salient-pole ratio is not 1, thesynchronous motor can be controlled at a high rotational speed even byan inexpensive computing unit, and the scope of application can beexpanded to a synchronous motor having salient-pole properties.

[0032] In the control apparatus for a synchronous motor according to thenext invention based on the above invention, the adaptive observer has afeedback gain which is given by a function of the estimated rotationalspeed such that transmission characteristics from a rotational speederror of the synchronous motor to an estimated magnetic flux error areaveraged in a frequency area.

[0033] According to this invention, since the adaptive observer has thefeedback gain which is given by the function of the estimated rotationalspeed such that the transmission characteristics from the rotationalspeed error of the synchronous motor to the estimated magnetic fluxerror are averaged in the frequency area, the pole of the synchronousmotor can be arbitrary set even if the synchronous motor is driven at alow rotational speed, and the synchronous motor can be stably controlledwithout deteriorating the accuracy of magnetic flux estimation.

[0034] In the control apparatus for a synchronous motor according to thenext invention based on the above invention, the adaptive observercalculates an estimated rotational speed based on a q-axis component ofa deviation between a current on the rotational biaxial coordinates (d-qaxis) and the estimated current.

[0035] According to this invention, since the estimated rotational speedcan be calculated based on the q-axis component of the deviation betweenthe current on the rotational biaxial coordinates (d-q axis) and theestimated current, the number of times of multiplication and divisionrequired for calculation can be reduced by omitting a product betweenthe q-axis component of the deviation between the current and theestimated current and an estimated rotor magnetic flux, and acalculation time can be shortened.

[0036] In the control apparatus for a synchronous motor according to thenext invention based on the above invention, the adaptive observercalculates an estimated rotational speed based on a value obtained bydividing the q-axis component of the deviation between the current onthe rotational biaxial coordinates (d-q axis) and the estimated currentby the estimated rotor magnetic flux.

[0037] According to this invention, since the estimated rotational speedis calculated based on the value obtained by dividing the q-axiscomponent of the deviation between the current on the rotational biaxialcoordinates (d-q axis) and the estimated current by the estimated rotormagnetic flux, even though the rotor magnetic flux changes depending ona temperature, an estimated response of the rotational speed can be keptconstant.

[0038] The control apparatus for a synchronous motor according to thenext invention based on the above invention, includes a speed controllerwhich outputs a current command on the rotational biaxial coordinates(d-q axis) such that the current command is equal to a rotational speedcommand based on at least one value of an estimated rotational speedobtained from the adaptive observer and the angular frequency.

[0039] According to this invention, since the speed controller whichprovides the current command on the rotational biaxial coordinates (d-qaxis) such that the current command is equal to the rotational speedcommand based on at least one value of the estimated rotational speedobtained from the adaptive observer and the angular frequency isarranged, the synchronous motor can be controlled in speed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0040]FIG. 1 is a block diagram which shows the entire configuration ofa control apparatus for a synchronous motor according to a firstembodiment of the present invention,

[0041]FIG. 2 is a block diagram which shows the configuration of anadaptive observer according to the first embodiment,

[0042]FIG. 3 is a diagram which shows the configuration of an electricmotor model 11 a,

[0043]FIG. 4 is a diagram which shows the configuration of an adaptiveobserver 9 b,

[0044]FIG. 5 is a diagram which shows the configuration of an electricmotor model 11 b,

[0045]FIG. 6 is a diagram which shows the configuration of an adaptiveobserver 9 c,

[0046]FIG. 7 is a diagram which shows the configuration of an electricmotor model 11 c,

[0047]FIG. 8 is a block diagram which shows a synchronous motor 1 whensystem noise and measurement noise are input as disturbance,

[0048]FIG. 9 shows examples of feedback gains h11, h12, h21, h22, h31,h32, h41, and h42 obtained by equation (46),

[0049]FIG. 10 is a graph on which magnitudes of the maximum pole of theadaptive observer when an arbitrary positive number ε is changed areplotted,

[0050]FIG. 11 shows examples of feedback gains h11, h12, h21, h22, h31,h32, h41, and h42 related to a synchronous motor in which a salient-poleratio is not 1,

[0051]FIG. 12 is a graph on which magnitudes of the maximum pole of anadaptive observer when the positive number ε is changed are plotted,

[0052]FIG. 13 is a diagram which shows the internal configuration of again computing unit 15 d,

[0053]FIG. 14 is a diagram which shows the configuration of a knownspeed control unit which amplifies a deviation between a rotationalspeed command and an estimated rotational speed,

[0054]FIG. 15 is a block diagram which shows the entire configuration ofa conventional control apparatus for a synchronous motor, and

[0055]FIG. 16 is a diagram which shows the internal configuration of aconventional adaptive observer 9.

BEST MODE FOR CARRYING OUT THE INVENTION

[0056] Preferred embodiments of a receiver according to this inventionwill be explained below with reference to the accompanying drawings.

[0057] First Embodiment:

[0058] Derivation of an adaptive observer used in the present inventionwill be explained below. When electric motor models expressed byequations (4), (5), and (10) are converted into rotational biaxialcoordinates (d-q axis) rotated at an arbitrary angular frequency w, thefollowing equations (11) to (13) are obtained. $\begin{matrix}{{\frac{}{t}\begin{pmatrix}{id0} \\{iq0} \\{pdr0} \\{pqr0}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & \frac{wr0}{L} \\{- w} & {- \frac{R}{L}} & {- \frac{wr0}{L}} & 0 \\0 & 0 & 0 & {w - {wr0}} \\0 & 0 & {{- w} + {wr0}} & 0\end{pmatrix}\begin{pmatrix}{id0} \\{iq0} \\{pdr0} \\{pqr0}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{L} & 0 \\0 & \frac{1}{L} \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} & * \\{vq} & *\end{pmatrix}} - \begin{pmatrix}{e1} \\{e2} \\{e3} \\{e4}\end{pmatrix}}} & (11) \\{{wr0} = {\left( {{kp} + \frac{ki}{s}} \right)\left( {{{ed} \cdot {pqr0}} - {{eq} \cdot {pdr0}}} \right)}} & (12) \\{\begin{pmatrix}{e1} \\{e2} \\{e3} \\{e4}\end{pmatrix} = {\begin{pmatrix}{g1} & {- {g2}} \\{g2} & {g1} \\{g3} & {- {g4}} \\{g4} & {g3}\end{pmatrix}\begin{pmatrix}{ed} \\{eq}\end{pmatrix}}} & (13)\end{matrix}$

[0059] The equations (11) to (13) are satisfied on the rotationalbiaxial coordinate axis rotated at the arbitrary angular frequency w.Therefore, obviously these equations are also satisfied on therotational biaxial coordinate axis rotated at the angular frequency wgiven by the following equation (14), $\begin{matrix}{w = {{wr0} - \frac{e4}{pdr0}}} & (14)\end{matrix}$

[0060] Calculation of the angular frequency w given by the equation (14)corresponds to calculation in which the angular frequency w iscalculated such that a q-axis component of an estimated rotor magneticflux is zero. Therefore, in this embodiment, the rotational biaxialcoordinate axis rotated at the angular frequency w given by the equation(14) is defined as a d-q axis.

[0061] When the equation (14) is substituted to the fourth line of theequation (11), the following equation (15) is obtained. $\begin{matrix}{{\frac{}{t}{pqr0}} = 0} & (15)\end{matrix}$

[0062] In the present invention, the direction of an estimated rotormagnetic flux vector is made equal to the direction of the d-axis. Atthis time, since the following equation (16) is established, when theequations (15) and (16) are substituted to the equations (11) and (12),the following equations (17) and (18) are obtained,

pqr0=0  (16) $\begin{matrix}{\begin{pmatrix}{e1} \\{e2} \\{e3} \\{e4}\end{pmatrix} = {\begin{pmatrix}{g1} & {- {g2}} \\{g2} & {g1} \\{g3} & {- {g4}} \\{g4} & {g3}\end{pmatrix}\begin{pmatrix}{ea} \\{eb}\end{pmatrix}}} & (10)\end{matrix}$

[0063] With the configuration described above, the adaptive observer 9outputs the estimated rotor magnetic fluxes par0 and pbr0 and theestimated rotational speed wr0.

[0064] In the conventional control apparatus for a synchronous motor,the frequency components of the voltages va* and vb* input to theadaptive observer become high when the synchronous motor operates at ahigh rotational speed because the adaptive observer is constituted onthe two static axes. Therefore, when the calculation of the adaptiveobserver is realized by a computer, sampling of the voltages va* and vb*must be performed at a very short cycle to drive the synchronous motorat a high rotational speed.

[0065] The conventional control apparatus for a synchronous motor cannotbe easily applied to a synchronous motor in which an inductance Ld inthe direction (d-axis direction) of a rotor magnetic flux is not equalto an inductance Lq in the direction (q-axis direction) perpendicular tothe direction of the rotor magnetic flux, i.e., a synchronous motor inwhich a salient-pole ratio is not 1. In the synchronous motor in whichthe salient-pole ratio is not $\begin{matrix}{{\frac{}{t}\begin{pmatrix}{id0} \\{iq0} \\{pdr0}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 \\{- w} & {- \frac{R}{L}} & {- \frac{wr0}{L}} \\0 & 0 & 0 \\\quad & \quad & \quad\end{pmatrix}\begin{pmatrix}{id0} \\{iq0} \\{pdr0}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{L} & 0 \\0 & \frac{1}{L} \\0 & 0 \\\quad & \quad\end{pmatrix}\begin{pmatrix}{vd} & * \\{vq} & *\end{pmatrix}} - \begin{pmatrix}{e1} \\{e2} \\{e3}\end{pmatrix}}} & (17) \\{{wr0} = {\left( {{kp} + \frac{ki}{s}} \right)\left( {{eq} \cdot {pdr0}} \right)}} & (18)\end{matrix}$

[0066] Therefore, when the same calculation as that of the conventionaladaptive observer constituted by the equations (4) to (10) is performedbased on the equations (13), (14), (17), and (18), the calculation canbe performed on the rotational biaxial coordinate axis.

[0067] The voltage commands va* and vb* on the static biaxialcoordinates input to the conventional adaptive observer are AC. However,voltage commands vd* and vq* input to the adaptive observer constitutedby the equations (13), (14), (17), and (18) are DC quantities becausethe voltage commands vd* and vq* are variables on the rotational biaxialcoordinate axis.

[0068] Therefore, when the calculation of the conventional adaptiveobserver is realized by a computing unit, sampling of the voltages va*and vb* must be performed at a very short cycle to drive the synchronousmotor at a high rotational speed. However, the adaptive observerconstituted by the equations (13), (14), (17), and (18) can solve thisproblem because the voltage commands vd* and vq* are DC quantities.

[0069] The configuration of the control apparatus for a synchronousmotor according to the first embodiment will be explained below. FIG. 1is a diagram which shows the configuration of the control apparatus fora synchronous motor according to the first embodiment. In FIG. 1,reference numerals 1, 2, 3, and 4 denote the same parts in theconventional apparatus, and an explanation thereof will be omitted.Reference numerals 5 a and 8 a denote coordinate converters, referencenumeral 9 a denotes an adaptive observer, and 17 denotes an integrator.

[0070] The coordinate converter 5 a coordinate-converts a d-axis voltagecommand vd* and a q-axis voltage command vq* on the rotational biaxialcoordinate axis (d-q axis) into three-phase voltage commands vu* vv*,and vw* based on a rotational position th0 obtained from the integrator17.

[0071] The coordinate converters 8 a outputs an a-axis current ia and ab-axis current ib on the static biaxial coordinates (a-b axis) and ad-axis current id and a q-axis current iq on the rotational biaxialcoordinates (d-q axis) based on a U-phase current iu and a V-phasecurrent iv obtained from the current detectors 2 and the rotationalposition th0 obtained from the integrator 17.

[0072] The adaptive observer 9 a outputs an estimated rotor magneticflux pdr0, the angular frequency w, and an estimated rotational speedwr0 based on the d-axis voltage command vd* and the q-axis voltagecommand vq* on the rotational biaxial coordinate axis (d-q axis) and thed-axis current command id and the q-axis current command iq on therotational biaxial coordinate axis (d-q axis).

[0073] The integrator 17 integrates the angular frequency w obtainedfrom the adaptive observer 9 a to output the rotational position th0.

[0074]FIG. 2 is a diagram which shows the internal configuration of theadaptive observer 9 a. In this figure, reference numeral 15 denotes thesame part in the conventional apparatus, and an explanation thereof willbe omitted. Reference numeral 11 a denotes an electric motor model, 12 aand 13 a denote subtractors, 14 a denotes a speed identifier, and 16 adenotes a deviation amplifier.

[0075] The electric motor model 11 a calculates a d-axis estimatedcurrent id0 and a q-axis estimated current iq0 on the rotational biaxialcoordinates (d-q axis), the estimated rotor magnetic flux pdr0, and theangular frequency w according to equations (14) and (17) based on thed-axis voltage command vd* and the q-axis voltage command vq* on therotational biaxial coordinates (d-q axis), the estimated rotor speedwr0, and deviations e1, e2, e3, and e4 (to be described later).

[0076] The subtractor 12 a outputs a result obtained by subtracting thed-axis current id from the d-axis estimated current id0 as a d-axiscurrent deviation ed. The subtractor 13 a outputs a result obtained bysubtracting the q-axis current iq from the q-axis estimated current iq0as a q-axis current deviation eq.

[0077] The speed identifier 14 a outputs the estimated rotational speedwr0 according to equation (18) based on the currents pdr0 and eq. Thegain computing unit 15 outputs gains g1, g2, g3, and g4 according toequations (6) to (9) based on the estimated rotational speed wr0.

[0078] The deviation amplifier 16 a amplifies the current deviations edand eq by the gains g1, g2, g3, and g4 to output the deviations e1, e2,e3, and e4. More specifically, the deviation amplifier 16 a outputs thedeviations e1, e2, e3, and e4 to the electric motor model 11 a accordingto the equation (13).

[0079] With the above configuration, the adaptive observer 9 a outputsthe estimated rotor magnetic flux pdr0, the angular frequency w, and theestimated rotational speed wr0.

[0080]FIG. 3 is a diagram which shows the configuration of the electricmotor model 11 a. In this figure, reference numerals 18 and 19 denotematrix gains, 20 to 23 denote adder-subtractors, 24 to 26 denoteintegrators, and 27 denote a divider.

[0081] The matrix gain 18 outputs a calculation result of the secondterm of the right side of the equation (17) based on the input voltagecommands vd* and vq*. The matrix gain 19 outputs a calculation result ofthe first term of the right side of the equation (17) based on the inputangular frequency w, the input estimated rotational speed wr0, the inputestimated currents iq0 and iq0, and the input estimated rotor magneticflux pdr0.

[0082] The adder-subtractors 20 to 22 add and subtract the first term,the second term, and the third term of the right side of the equation(17) to output d/dt id0, d/dt iq0, and d/dt pdr0, respectively. Theintegrator 24 outputs id0 by integrating the d/dt id0. The integrator 25outputs iq0 by integrating the d/dt iq0. The integrator 26 outputs pdr0by integrating the d/dt pdr0.

[0083] The divider 27 outputs a calculation result of the second term ofthe right side of the equation (14) based on the input e4 and pdr0. Thesubtractor 23 subtracts an output from the divider 27 from the estimatedrotational speed wr0 to output the right side of the equation (14),i.e., the angular frequency w.

[0084] With the above configuration, the electric motor model 9 acalculates the d-axis estimated current id0 and the q-axis estimatedcurrent iq0 on the rotational biaxial coordinates (d-q axis), theestimated rotor magnetic flux pdr0, and the angular frequency waccording to the equations (14) and (17).

[0085] According to this embodiment, the adaptive observer isconstituted on the rotational two axes, and therefore even though thesynchronous motor operates at a high rotational speed, the frequencycomponents of the voltages vd* and vq* input to the adaptive observerare DC components. For this reason, even though calculation of theadaptive observer is realized by a computing unit, sampling of thevoltages vd* and vq* need not be performed at a very short cycle.Therefore, even though an inexpensive computing unit is used, thesynchronous motor can be controlled at a high rotational speed.

[0086] Second Embodiment:

[0087] In the first embodiment, the apparatus can be applied to asynchronous motor the inductance of which has no salient-poleproperties. However, the apparatus cannot be directly applied to thesynchronous motor which has salient-pole properties without any changeto the apparatus. Therefore, in the second embodiment, a controlapparatus for a synchronous motor which can be applied to a synchronousmotor which has salient-pole properties will be explained.

[0088] As is well known, in the synchronous motor having salient-poleproperties, an inductance in the direction of the rotor magnetic flux isdifferent from an inductance in the direction perpendicular to thedirection of the rotor magnetic flux, and therefore the inductance inthe direction of the rotor magnetic flux is defined as Ld, and theinductance in the direction perpendicular to the direction of the rotormagnetic flux is defined as Lq in the following description.

[0089] In general, it is known that the following equation (19) holds onthe rotational biaxial coordinates (d-q axis) having a d-axis which isrotated in synchronism with the direction of the rotor magnetic flux,$\begin{matrix}{{\frac{}{t}\begin{pmatrix}{id} \\{iq} \\{pdr}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{Ld}} & {\frac{Lq}{Ld}w} & 0 \\{{- \frac{Ld}{Lq}}w} & {- \frac{R}{Lq}} & {- \frac{wr}{Lq}} \\0 & 0 & 0 \\\quad & \quad & \quad\end{pmatrix}\begin{pmatrix}{id} \\{iq} \\{pdr}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{Ld} & 0 \\0 & \frac{1}{Lq} \\0 & 0 \\\quad & \quad\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}}}} & (19)\end{matrix}$

[0090] Therefore, when the elements of the equations (17) and (19) arecompared with each other, based on an adaptive observer related to asynchronous motor having salient-pole properties, the followingequations (20), (21), and (22) can be derived, $\begin{matrix}{{\frac{}{t}\begin{pmatrix}{id0} \\{iq0} \\{pdr0}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{Ld}} & {\frac{Lq}{Ld}w} & 0 \\{{- \frac{Ld}{Lq}}w} & {- \frac{R}{Lq}} & {- \frac{wr0}{Lq}} \\0 & 0 & 0 \\\quad & \quad & \quad\end{pmatrix}\begin{pmatrix}{id0} \\{iq0} \\{pdr0}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{Ld} & 0 \\0 & \frac{1}{Lq} \\0 & 0 \\\quad & \quad\end{pmatrix}\begin{pmatrix}{vd} & * \\{vq} & *\end{pmatrix}} - \begin{pmatrix}{e01} \\{e02} \\{e03}\end{pmatrix}}} & (20) \\{w = {{wr0} - \frac{e04}{pdr0}}} & (21) \\{\begin{pmatrix}{e01} \\{e02} \\{e03} \\{e04}\end{pmatrix} = {\begin{pmatrix}{g11} & {g12} \\{g21} & {g22} \\{g31} & {g32} \\{g41} & {g42}\end{pmatrix}\begin{pmatrix}{ed} \\{eq}\end{pmatrix}}} & (22)\end{matrix}$

[0091] Although feedback gains are constituted by the four types ofelements g1 to g4 in the equation (13), the coefficients of the equation(21) constitute feedback gains with reference to eight types of elementsg11 to g41 obtained in consideration of a salient-pole ratio, e.g., thefollowing equations (23) to (30). $\begin{matrix}{{g11} = {{- \left( {k - 1} \right)}\frac{R}{Ld}}} & (23) \\{{g12} = {{- \left( {k - 1} \right)}\frac{Ld}{Lq}{wr0}}} & (24) \\{{g21} = {\left( {k - 1} \right)\frac{Lq}{Ld}{wr0}}} & (25) \\{{g22} = {{- \left( {k - 1} \right)}\frac{R}{Lq}}} & (26)\end{matrix}$

 g31=k R  (27)

g32=k L qwr0  (28)

g41=−k L dwr0  (29)

g42=k R  (30)

[0092] The configuration of the second embodiment merely uses asynchronous motor 1 b in place of the synchronous motor 1 and uses anadaptive observer 9 b in place of the adaptive observer 9 a in FIG. 1(not shown).

[0093] The synchronous motor 1 b has a permanent magnet as a rotor therotor magnetic flux of which is pdr. The inductance in the direction(d-axis direction) of the rotor magnetic flux is Ld, and the inductancein the direction (q-axis direction) perpendicular to the direction ofthe rotor magnetic flux is Lq.

[0094]FIG. 4 is a diagram which shows the configuration of the adaptiveobserver 9 b. In this figure, reference numerals 12 a, 13 a, and 14 adenote the same parts in the first embodiment, and an explanationthereof will be omitted. Reference numeral 11 b denotes an electricmotor model, 15 b denotes a gain computing unit, and 16 b denotes adeviation amplifier.

[0095] The electric motor model 11 b calculates a d-axis estimatedcurrent id0 and a q-axis estimated current iq0 on the rotational biaxialcoordinates (d-q axis), a d-axis estimated rotor magnetic flux pdr0, andan angular frequency w according to the equations (20) and (21) based onthe d-axis voltage command vd* and the q-axis voltage command vq* on therotational biaxial coordinates (d-q axis), the estimated rotationalspeed wr0, and deviations e1, e2, e3, and e4 (to be described later).

[0096] The gain computing unit 15 b outputs gains g11, g12, g21, g22,g31, g32, g41, and g42 according to the equations (23) to (30) based onthe estimated rotational speed wr0. The deviation amplifier 16 bamplifies the current deviations ed and eq by the gains g11, g12, g21,g22, g31, g32, g41, and g42 to output deviations e01, e02, e03, and e04.More specifically, the deviation amplifier 16 b outputs the deviationse01, e02, e03, and e04 to the electric motor model 11 b according to theequation (22).

[0097] With the above configuration, the adaptive observer 9 b outputsthe estimated rotor magnetic flux pdr0, the angular frequency w, and theestimated rotational speed wr0.

[0098]FIG. 5 is a diagram which shows the configuration of the electricmotor model 11 b. In this figure, reference numerals 20 to 27 denote thesame parts in the first embodiment, and an explanation thereof will beomitted. Reference numerals 18 b and 19 b denote matrix gains.

[0099] The matrix gain 18 b outputs a calculation result of the secondterm of the right side of the equation (20) based on the input voltagecommands vd* and vq*. The matrix gain 19 b outputs a calculation resultof the first term of the right side of the equation (20) based on theinput angular frequency w, the input estimated rotational speed wr0, theinput estimated currents id0 and iq0, and the input estimated rotormagnetic flux pdr0.

[0100] The adder-subtractors 20 to 22 add and subtract the first,second, and third terms of the right side of the equation (20) to outputd/dt id0, d/dt iq0, and d/dt pdr0, respectively. The divider 27 outputsa calculation result of the second term of the right side of theequation (21) based on the input e04 and pdr0. The subtractor 23subtracts the output of the divider 27 from the estimated rotationalspeed wr0 to output the right side of the equation (21), i.e., theangular frequency w.

[0101] With the above configuration, the electric motor model 9 bcalculates the d-axis estimated current id0 and the q-axis estimatedcurrent iq0 on the rotational biaxial coordinates (d-q axis), the d-axisestimated rotor magnetic flux pdr0, and the angular frequency waccording to the equations (20) and (21).

[0102] According to the second embodiment, as in the first embodiment,the synchronous motor can be controlled at a high rotational speed by aninexpensive computing unit, and the scope of application can be expandedto the synchronous motor having a salient-pole properties.

[0103] Third Embodiment:

[0104] In the second embodiment, state variables of the adaptiveobserver 9 b are handled as id0, iq0, pdr0, pqr0 (=0). However, thestate variables may be handled as pds0, pqs0, pdr0, and pqr0. Referencesymbols pds0 and pqs0 denote a d-axis component and a q-axis componentof estimated armature reaction on a rotational biaxial coordinatesdefined by the following equation (31), $\begin{matrix}{\begin{pmatrix}{pds0} \\{pqs0}\end{pmatrix} = {\begin{pmatrix}{Ld} & 0 \\0 & {Lq}\end{pmatrix}\begin{pmatrix}{ids0} \\{iqs0}\end{pmatrix}}} & (31)\end{matrix}$

[0105] When the equation (31) is substituted into the equations (20) to(22), the following equations (32) to (35) are obtained, $\begin{matrix}{{\frac{}{t}\begin{pmatrix}{pds0} \\{pqs0} \\{pdr0}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{Ld}} & w & 0 \\{- w} & {- \frac{R}{Lq}} & {- {wr0}} \\0 & 0 & 0\end{pmatrix}\begin{pmatrix}{pds0} \\{pqs0} \\{pdr0}\end{pmatrix}} + \begin{pmatrix}{{vd}*} \\{{vq}*} \\0\end{pmatrix} - \begin{pmatrix}{f1} \\{f2} \\{f3}\end{pmatrix}}} & (32) \\{w = {{wr0} - \frac{f4}{pdr0}}} & (33) \\{\begin{pmatrix}{f1} \\{f2} \\{f3} \\{f4}\end{pmatrix} = {\begin{pmatrix}{h11} & {h12} \\{h21} & {h22} \\{h31} & {h32} \\{h41} & {h41}\end{pmatrix}\begin{pmatrix}{ed} \\{eq}\end{pmatrix}}} & (34) \\{\begin{pmatrix}{id0} \\{iq0}\end{pmatrix} = {\begin{pmatrix}\frac{1}{Ld} & 0 & 0 \\0 & \frac{1}{Lq} & 0\end{pmatrix}\begin{pmatrix}{pds0} \\{pqs0} \\{pdr0}\end{pmatrix}}} & (35)\end{matrix}$

[0106] where

[0107] h11=Ld g11, h12=Ld g12

[0108] h21=Lq g 21, h22=Lq g22

[0109] h31=g31, h32=g32

[0110] h41=g41, h42=q42

[0111] The configuration of the third embodiment merely uses an adaptiveobserver 9 c in place of the adaptive observer 9 a in FIG. 1. FIG. 6 isa diagram which shows the configuration of the adaptive observer 9 c. InFIG. 6, reference numerals 12 a, 13 a, and 14 a denote the same parts inthe first and second embodiments, and an explanation thereof will beomitted. Reference numeral 11 c denotes an electric motor model, 15 cdenotes a gain computing unit, and 16 c denotes a deviation amplifier.

[0112] The electric motor model 11 c calculates a d-axis estimatedcurrent id0 and a q-axis estimated current iq0 on the rotational biaxialcoordinates (d-q axis), a d-axis estimated rotor magnetic flux pdr0, andan angular frequency w according to equations (32) and (33) based on thed-axis voltage command vd* and the q-axis voltage command vq* on therotational biaxial coordinates (d-q axis), the estimated rotationalspeed wr0, and deviations f1, f2, f3, and f4 (to be described later).

[0113] The gain computing unit 15 c outputs gains h11, h12, h21, h22,h31, h32, h41, and h42 based on the estimated rotational speed wr0. Thedeviation amplifier 16 c amplifies the current deviations ed and eq bythe gains h11, h12, h21, h22, h31, h32, h41, and h42 to outputdeviations f1, f2, f3, and f4. More specifically, the deviationamplifier 16 c outputs the deviations f1, f2, f3, and f4 to the electricmotor model 11 c according to the equation (34).

[0114] With the above configuration, the adaptive observer 9 c outputsthe estimated rotor magnetic flux pdr0, the angular frequency w, and theestimated rotational speed wr0.

[0115]FIG. 7 is a diagram which shows the configuration of the electricmotor model 11 c. In this figure, reference numeral 30 denotes a gain,31 and 32 denote matrix gains, 33 and 34 denote adder-subtractors, 35denotes a subtractor, 36 to 38 denote integrators, and 39 denotes adivider.

[0116] The matrix gain 31 outputs calculation results of the first andsecond lines of the first term of the right side of the equation (32)based on the input angular frequency w, the input estimated rotationalspeed wr0, the input estimated armature reactions pds0 and pqs0, and theinput estimated rotor magnetic flux pdr0.

[0117] The adder-subtractors 33 and 34 add and subtract the second andthird lines of the first, second, and third terms of the right side ofthe equation (32) to output d/dt pds0 and d/dt pqs0, respectively. Thegain 30 makes the deviation f3-1 times to calculate the third line ofthe right side of the equation (32), thereby outputting d/dt pdr0.

[0118] The integrators 36 to 38 integrate the d/dt pds0, d/dt pqs0, andd/dt pdr0 to output pds0, pqs0, and pdr0. The matrix gain 32 outputsestimated currents id0 and iq0 according to the equation (35) based onthe pds0 and pqs0.

[0119] The divider 39 outputs a calculation result of the second term ofthe right side of the equation (33) based on the input f4 and pdr0. Thesubtractor 35 subtracts an output of the divider 39 from the estimatedrotational speed wr0 to output the right side of the equation (33),i.e., the angular frequency w.

[0120] With the above configuration, the electric motor model 9 ccalculates the d-axis estimated current id0 and the q-axis estimatedcurrent iq0 on the rotational biaxial coordinates (d-q axis), theestimated rotor magnetic flux pdr0, and the angular frequency waccording to the equations (32), (33), and (35).

[0121] Although the third embodiment has state variables which aredifferent from those of the second embodiment, the third embodiment isessentially equivalent to the second embodiment. Therefore, as in thesecond embodiment, the synchronous motor can be controlled at a highrotational speed even by an inexpensive computing unit. In addition, thescope of application can be expanded to the synchronous motor havingsalient-pole properties.

[0122] Fourth Embodiment:

[0123] In the first embodiment, the feedback gains of the adaptiveobserver are determined to be in proportion to the unique pole of thesynchronous motor. However, when the gains g1, g2, g3, and g4 expressedby the equations (6) to (9) in the adaptive observer are determined, andwhen the synchronous motor is driven at a low rotational speed, the poleof the synchronous motor decreases. Accordingly, the pole of theadaptive observer also decreases. For this reason, the response of anestimated magnetic flux is deteriorated, and the characteristics of thecontrol system itself are also deteriorated. In addition, when an actualrotational speed wr is deviated from the estimated rotational speed wr0,the estimation accuracy of the estimated magnetic flux is deteriorateddisadvantageously.

[0124] Therefore, the fourth embodiment will explain a method ofaveraging transmission characteristics between a speed error of thesynchronous motor and a magnetic flux estimation error in a frequencyarea. In a control apparatus for a synchronous motor which uses thismethod, deterioration in accuracy of magnetic flux estimation caused bythe deviation between the actual rotational speed wr and the estimatedrotational speed wr0 can be suppressed, and the magnitude of the pole ofthe observer can be kept at a desired value. For this reason, arotational speed can be preferably estimated.

[0125] The method of designing a gain will be explained below. Anequation of the synchronous motor on rotational biaxial coordinatesrotated at an arbitrary frequency w as described above is given by thefollowing equation, $\begin{matrix}{{\frac{}{t}\begin{pmatrix}{id} \\{iq} \\{pdr} \\{pqr}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & \frac{wr}{L} \\{- w} & {- \frac{R}{L}} & {- \frac{wr}{L}} & 0 \\0 & 0 & 0 & {w - {wr}} \\0 & 0 & {{- w} + {wr}} & 0\end{pmatrix}\begin{pmatrix}{id} \\{iq} \\{pdr} \\{pqr}\end{pmatrix}} + {\begin{pmatrix}\frac{1}{L} & 0 \\0 & \frac{1}{L} \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}}}} & (36)\end{matrix}$

[0126] Armature reactions pds and pqs are defined by equation (37). Thisequation is substituted to the state equation expressed by the equation(36), the following equation (38) is obtained, $\begin{matrix}{\begin{pmatrix}{pds} \\{pqs}\end{pmatrix} = {\begin{pmatrix}L & 0 \\0 & L\end{pmatrix}\begin{pmatrix}{id} \\{iq}\end{pmatrix}}} & (37) \\{{\frac{}{t}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} = {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & {wr} \\{- w} & {- \frac{R}{L}} & {- {wr}} & 0 \\0 & 0 & 0 & {w - {wr}} \\0 & 0 & {{- w} + {wr}} & 0\end{pmatrix}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} + {\begin{pmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}}}} & (38)\end{matrix}$

[0127] When the rotational speed wr changes by Δwr, the equation (38)changes as expressed by the following equation (39), $\begin{matrix}\begin{matrix}{{\frac{}{t}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} = \quad {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & {{wr} + {\Delta \quad {wr}}} \\{- w} & {- \frac{R}{L}} & {{- {wr}} - {\Delta \quad {wr}}} & 0 \\0 & 0 & 0 & {w - {wr} - {\Delta \quad {wr}}} \\0 & 0 & {{- w} + {wr} + {\Delta \quad {wr}}} & 0\end{pmatrix}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} +}} \\{\quad {\begin{pmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}}} \\{= \quad {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & {wr} \\{- w} & {- \frac{R}{L}} & {- {wr}} & 0 \\0 & 0 & 0 & {w - {wr}} \\0 & 0 & {{- w} + {wr}} & 0\end{pmatrix}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} + {\begin{pmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}} +}} \\{\quad {\begin{pmatrix}0 & 1 \\{- 1} & 0 \\0 & {- 1} \\1 & 0\end{pmatrix}\Delta \quad {{wr}\begin{pmatrix}{pdr} \\{pqr}\end{pmatrix}}}} \\{= \quad {{\begin{pmatrix}{- \frac{R}{L}} & w & 0 & {wr} \\{- w} & {- \frac{R}{L}} & {- {wr}} & 0 \\0 & 0 & 0 & {w - {wr}} \\0 & 0 & {{- w} + {wr}} & 0\end{pmatrix}\begin{pmatrix}{pds} \\{pqs} \\{pdr} \\{pqr}\end{pmatrix}} + {\begin{pmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{pmatrix}\begin{pmatrix}{vd} \\{vq}\end{pmatrix}} +}} \\{\quad {\begin{pmatrix}0 & 1 \\{- 1} & 0 \\0 & {- 1} \\1 & 0\end{pmatrix}\begin{pmatrix}{w2d} \\{w2q}\end{pmatrix}}}\end{matrix} & (39) \\{{{where}\quad \begin{pmatrix}{w2d} \\{w2q}\end{pmatrix}} = \begin{pmatrix}{\Delta \quad {wr}} & {pdr0} \\{\Delta \quad {wr}} & {pqr0}\end{pmatrix}} & \quad\end{matrix}$

[0128] Therefore, it can be understood that the equation (39) is anequation in which system noise and measurement noise expressed byequation (40) are input as disturbance to an ideal synchronous motorexpressed by the equation (38). $\begin{matrix}{{{system}\quad {{noise}:{\begin{pmatrix}0 & 1 \\{- 1} & 0 \\0 & {- 1} \\1 & 0\end{pmatrix}\begin{pmatrix}{w2d} \\{w2q}\end{pmatrix}}}}\quad {{measurement}\quad {{noise}:{\begin{pmatrix}ɛ & 0 \\0 & ɛ\end{pmatrix}{w1}}}}} & (40)\end{matrix}$

[0129]FIG. 8 is a block diagram of the synchronous motor 1 used at thistime.

[0130] As described above, disturbance occurring when a deviation of Δwris produced between the rotational speed and the estimated rotationalspeed is stereotyped by the equation (40), and feedback gains h11, h12,h21, h22, h31, h32, h41, and h42 are determined such that transmissionmatrix gains from the disturbance expressed by the equation (40) to theestimated magnetic flux error are minimum. In this state, even though adeviation is produced between the rotational speed and the estimatedrotational speed, an influence to estimation of a rotor magnetic fluxcaused by the speed deviation can be suppressed.

[0131] Matrixes A, C, Q, and R are defined by equations (41), (42),(43), and (44). The matrix A is obtained by substituting w=0 to thefirst term of the right side of the equation (38), the matrix C includesa magnet flux to a current, the matrix Q is a covariance matrix relatedto system noise, and the matrix R is a covariance matrix related tomeasurement noise. $\begin{matrix}{A = \begin{pmatrix}{- \frac{R}{L}} & 0 & 0 & {wr} \\0 & {- \frac{R}{L}} & {- {wr}} & 0 \\0 & 0 & 0 & {- {wr}} \\0 & 0 & {wr} & 0\end{pmatrix}} & (41) \\{C = \begin{pmatrix}\frac{1}{L} & 0 & 0 & 0 \\0 & \frac{1}{L} & 0 & 0\end{pmatrix}} & (42) \\{Q = {{\begin{pmatrix}0 & 1 \\{- 1} & 0 \\0 & {- 1} \\1 & 0\end{pmatrix}\begin{pmatrix}0 & 1 \\{- 1} & 0 \\0 & {- 1} \\1 & 0\end{pmatrix}^{T}} = \begin{pmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\{- 1} & 0 & 1 & 0 \\0 & {- 1} & 0 & 1\end{pmatrix}}} & (43) \\{R = {{\begin{pmatrix}ɛ & 0 \\0 & ɛ\end{pmatrix}\begin{pmatrix}ɛ & 0 \\0 & ɛ\end{pmatrix}^{T}} = \begin{pmatrix}ɛ^{2} & 0 \\0 & ɛ^{2}\end{pmatrix}}} & (44)\end{matrix}$

[0132] A positive definite unique solution P which satisfies a Riccatiequation expressed by the equation (44) is obtained. When the feedbackgains h11, h12, h21, h22, h31, h32, h41, and h42 are given by theequation (45), even though a deviation is produced between therotational speed and the estimated rotational speed, an influence toestimation of a rotor magnetic flux caused by the speed deviation can besuppressed.

PA ^(T) +AP−PC ^(T) R ⁻¹ CP ^(T) +Q=0  (45)

[0133] However, since the matrix A includes the rotational speed wr, thefeedback gains h11, h12, h21, h22, h31, h32, h41, and h42 are functionsof the rotational speeds.

[0134] The feedback gains h11, h12, h21, h22, h31, h32, h41, and h42 maybe prepared as a table with respect to the respective rotational speeds,and the feedback gains h11, h12, h21, h22, h31, h32, h41, and h42 may bedetermined as functions of estimated rotational speeds in place of therotational speeds.

[0135]FIG. 9 shows examples of the feedback gains h11, h12, h21, h22,h31, h32, h41, and h42 obtained by giving an appropriate number εaccording to equation (46). The relationships shown in FIG. 9 are merelyprepared in a gain computing unit as a table. Since the gain computingunit cannot detect an actual rotational speed, the functions of theestimated rotational speeds may be set. $\begin{matrix}{\begin{pmatrix}{h11} & {h12} \\{h21} & {h22} \\{h31} & {h32} \\{h41} & {h42}\end{pmatrix} = {{PC}^{T}R^{- 1}}} & (46)\end{matrix}$

[0136]FIG. 10 is a graph on which magnitudes of the maximum pole of theadaptive observer when an arbitrary positive number ε is changed areplotted. As is apparent from FIG. 10, when the magnitude of ε ischanged, the magnitude of the maximum pole of the adaptive observer alsochanges. When this phenomenon is used, the magnitude of the pole of theobserver can be determined to be a desired value.

[0137] As is apparent from FIG. 9, in a synchronous motor in which asalient-pole ratio is 1 like the first embodiment, equations (47) to(50) are satisfied.

h11=h22  (47)

h21=−h12  (48)

h31=h42  (49)

h41=−h32  (50)

[0138] In the synchronous motor in which the salient-pole ratio is 1,the equation (37) is satisfied. For this reason, g1 to g4 in the gaincomputing unit in FIG. 2 are given by equations (51) to (54),transmission matrix gains from the disturbance expressed by the equation(40) to the estimated magnetic flux error can be minimized.$\begin{matrix}{{g1} = \frac{h11}{L}} & (51) \\{{g2} = \frac{h21}{L}} & (52) \\{{g3} = {h31}} & (53) \\{{g4} = {h41}} & (54)\end{matrix}$

[0139] According to the fourth embodiment, the pole of the synchronousmotor can be arbitrarily set even though the synchronous motor is drivenat a low rotational speed, and the gains are appropriate to performstate estimation when the estimated rotational speed is deviated fromthe actual rotational speed. For this reason, the synchronous motor canbe stably controlled without deteriorating the accuracy of magnetic fluxestimation.

[0140] Fifth Embodiment:

[0141] In the fourth embodiment, the control apparatus related to thesynchronous motor in which the salient-pole ratio is 1 has beenexplained. However, the present invention can also be applied to thecontrol apparatus for a synchronous motor in which a salient-pole ratiois not 1 and which is described in the third embodiment.

[0142] More specifically, a solution P of the Riccati equation (45) iscalculated by using equations (55) and (56) obtained in consideration ofa salient-pole ratio without using the equations (41) and (42), and thesolution P may be substituted to the equation (46). $\begin{matrix}{A = \begin{pmatrix}{- \frac{R}{Ld}} & 0 & 0 & {wr} \\0 & {- \frac{R}{Lq}} & {- {wr}} & 0 \\0 & 0 & 0 & {- {wr}} \\0 & 0 & {wr} & 0\end{pmatrix}} & (55) \\{C = \begin{pmatrix}\frac{1}{Ld} & 0 & 0 & 0 \\0 & \frac{1}{Lq} & 0 & 0\end{pmatrix}} & (56)\end{matrix}$

[0143]FIG. 11 shows examples of feedback gains h11, h12, h21, h22, h31,h32, h41, and h42 which can be obtained by giving an appropriate numberε according to the equation (46) and which is related to a synchronousmotor 1 a in which the salient-pole ratio is not 1.

[0144]FIG. 12 is a graph on which magnitudes of the maximum pole of anadaptive observer when an arbitrary positive number ε is changed. As isapparent from FIG. 12, when the magnitude of ε is changed, the magnitudeof the maximum pole of the adaptive observer also changes. In theconfiguration of the apparatus, the gain computing unit 15 c may bemerely replaced with a gain computing unit 15 d in FIG. 6 of the fourthembodiment.

[0145]FIG. 13 is a diagram which shows the internal configuration of thegain computing unit 15 d in the fifth embodiment. Reference numerals 40to 47 denote gain tables. The gain table 40 stores the relation of thefeedback gain h11 derived in advance shown in FIG. 11 and outputs thevalue of the feedback gain h11 based on the input estimated rotationalspeed wr0. Similarly, the gain tables 41 to 47 store the relations ofthe feedback gains h12, h21, h22, h31, h32, h41, and h42 derived inadvance and shown in FIG. 11, and output the values of the feedbackgains h21, h21, h22, h31, h32, h41, and h42 based on the input estimatedrotational speed wr0, respectively.

[0146] According to this embodiment, even in the synchronous motor inwhich the salient-pole ratio is not 1 is rotated at a low rotationalspeed, the pole of the synchronous motor can be arbitrarily set, andgains are appropriate to perform state estimation when an estimatedrotational speed is deviated from an actual rotational speed. For thisreason, the synchronous motor can be stably controlled withoutdeteriorating the accuracy of magnetic flux estimation.

[0147] Sixth Embodiment:

[0148] In the above embodiment, although the speed identifier 14performs calculation based on the equation (18), the right side of theequation (18) may be multiplied and divided by an arbitrary positivenumber. For example, since the rotor magnetic flux pdr and the estimatedrotor magnetic flux pdr0 are positive numbers, the estimated rotationalspeed wr0 may be given by equation (57) or equation (58) obtained bydividing the equation (18) by pdr0 or (pdr0)^ 2. $\begin{matrix}{{wr0} = {\left( {{kp} + \frac{ki}{s}} \right)\frac{eq}{pdr0}}} & (57) \\{{wr0} = {\left( {{kp} + \frac{ki}{s}} \right){eq}}} & (58)\end{matrix}$

[0149] When the estimated rotational speed wr0 is given by using theequation (58), even though the rotor magnetic flux pdr changes dependingon a temperature, an estimation response of a rotational speed can bekept constant. When the estimated rotational speed wr0 is given by usingthe equation (58), the number of times of multiplication and divisionrequired for calculation can be reduced. For this reason, calculationtime can be shortened.

[0150] Seventh Embodiment:

[0151] In the above embodiment, the apparatus which controls asynchronous motor by torque based on a torque command has beenexplained. However, as is well known, speed control maybe performed byusing a speed control unit which amplifies a deviation between arotational speed command and an estimated rotational speed.

[0152]FIG. 14 is a diagram which shows the configuration of a knownspeed control unit which amplifies a deviation between a rotationalspeed command and an estimated rotational speed. In this figure,reference numeral 48 denotes a subtractor, and 49 denotes a speedcontroller.

[0153] The subtractor 48 subtracts an estimated rotational speed wr0from a rotational speed command wr* and outputs a deviation obtainedthrough the subtraction to the speed controller 49. The speed controller49 outputs a q-axis current command iq* based on the deviation betweenthe rotational speed command wr* and the estimated rotational speed wr0.

[0154] According to the seventh embodiment, the synchronous motor can becontrolled in speed. When an angular frequency w is used in place of theestimated rotational speed wr0, the same effect as described above canbe obtained.

[0155] As has been described above, according to the present invention,the adaptive observer calculates the angular frequency w such that theq-axis component of the estimated rotor magnetic flux is zero, so thatthe adaptive observer can be constituted on rotational two axes. As aresult, even though the synchronous motor operates at a high rotationalspeed, the frequency components of the voltages vd* and vq* input to theadaptive observer are DC components. For this reason, sampling of thevoltages vd* and vq* need not be performed at a very short cycle eventhough calculation of the adaptive observer is realized by a computingunit. Therefore, the synchronous motor can be controlled at a highrotational speed by an inexpensive computing unit.

[0156] According to the next invention, since the adaptive observer hasthe electric motor model in which the salient-pole ratio is not 1, thesynchronous motor can be controlled at a high rotational speed even byan inexpensive computing unit, and the scope of application can beexpanded to a synchronous motor having salient-pole properties.

[0157] According to the next invention, since the control apparatusincludes the adaptive observer which has the feedback gain which isgiven by the function of the estimated rotational speed such that thetransmission characteristics from the rotational speed error of thesynchronous motor to the estimated magnetic flux error are averaged inthe frequency area, the pole of the synchronous motor can be arbitraryset even if the synchronous motor is driven at a low rotational speed,and the synchronous motor can be stably controlled without deterioratingthe accuracy of magnetic flux estimation.

[0158] According to the next invention, since the control apparatusincludes the adaptive observer which calculates the estimated rotationalspeed based on the q-axis component of the deviation between the currenton the rotational biaxial coordinates (d-q axis) and the estimatedcurrent, the number of times of multiplication and division required forcalculation can be reduced by omitting a product between the q-axiscomponent of the deviation between the current and the estimated currentand an estimated rotor magnetic flux. For this reason, calculation timecan be shortened.

[0159] According to the next invention, since the control apparatusincludes the adaptive observer which calculates the estimated rotationalspeed based on the value obtained by dividing the q-axis component ofthe deviation between the current on the rotational biaxial coordinates(d-q axis) and the estimated current by the estimated rotor magneticflux, even though the rotor magnetic flux changes depending on atemperature, an estimated response of the rotational speed can be keptconstant.

[0160] According to the next invention, since the control apparatusincludes the speed controller which gives the current command on therotational biaxial coordinates (d-q axis) such that the current commandis equal to the rotational speed command based on at least one value ofthe estimated rotational speed obtained from the adaptive observer andthe angular frequency w, the synchronous motor can be controlled inspeed.

INDUSTRIAL APPLICABILITY

[0161] As has been described above, the control apparatus for asynchronous motor according to the present invention is suitably used asa control apparatus used in various synchronous motors each including anadaptive observer.

1. A control apparatus for a synchronous motor comprising: a currentdetector which detects a current of a synchronous motor; a coordinateconverter which coordinate-converts the current obtained from thecurrent detector into a current on rotational biaxial coordinates (d-qaxis) rotated at an angular frequency; a current controller whichoutputs a voltage command on the rotational biaxial coordinates (d-qaxis) such that a current on the rotational biaxial coordinates (d-qaxis) follows a current command on the rotational biaxial coordinates(d-q axis); a coordinate converter which coordinate-converts the voltagecommand on the rotational biaxial coordinates (d-q axis) obtained fromthe current controller into three-phase voltage commands; an adaptiveobserver which calculates the angular frequency, an estimated current ofthe synchronous motor, an estimated rotor magnetic flux, and anestimated rotational speed based on the current on the rotationalbiaxial coordinates (d-q axis) and the voltage command on the rotationalbiaxial coordinates (d-q axis); and an inverter which applies a voltageto the synchronous motor based on the voltage command, wherein theadaptive observer calculates the angular frequency such that a q-axiscomponent of the estimated rotor magnetic flux is zero.
 2. The controlapparatus for a synchronous motor according to claim 1, wherein theadaptive observer has an electric motor model in which a salient-poleratio is not
 1. 3. The control apparatus for a synchronous motoraccording to claim 1, wherein the adaptive observer has a feedback gainwhich is given by a function of the estimated rotational speed such thattransmission characteristics from a rotational speed error of thesynchronous motor to an estimated magnetic flux error are averaged in afrequency area.
 4. The control apparatus for a synchronous motoraccording to claim 1, wherein the adaptive observer calculates theestimated rotational speed based on the q-axis component of thedeviation between the current on the rotational biaxial coordinates (d-qaxis) and the estimated current.
 5. The control apparatus for asynchronous motor according to claim 1, wherein the adaptive observercalculates the estimated rotational speed based on a value obtained bydividing the q-axis component of the deviation between the current onthe rotational biaxial coordinates (d-q axis) and the estimated currentby the estimated rotor magnetic flux.
 6. The control apparatus for asynchronous motor according to claim 1, comprising a speed controllerwhich outputs a current command on the rotational biaxial coordinates(d-q axis) such that the current command is equal to a rotational speedcommand based on at least one value of an estimated rotational speedobtained from the adaptive observer and the angular frequency.